A193929 Number of prime factors of n^4 + 1, counted with multiplicity.

0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 3, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 2, 2, 2, 3, 2, 4, 3, 3, 1, 3, 1, 3, 2, 3, 2, 3, 1, 3, 1, 2, 2, 4, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 2, 1, 3, 3, 4, 2, 4, 1, 2, 1, 4, 2, 4, 2, 3, 1, 3, 1, 3, 2, 3, 2, 4, 3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 1, 3, 2, 3, 3, 4, 2, 2, 2, 2, 2, 3, 1

Offset: 0

Author

Jonathan Vos Post, Aug 09 2011

Keywords

• nonn
• easy

Comments

This is to A193330 as A002523(n) = n^4+1 is to A002522(n) = n^2 + 1. a(n) = 2 when n^4+1 is prime, iff n is in A037896.

Examples

			a(9) = 3 because 9^4+1 = 6562 = 2 * 17 * 193, which has 3 prime factors, counted with multiplicity
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A002523, A193432, A193562.

Programs

Magma

[0] cat [&+[p[2]: p in Factorization(n^4+1)]:n in [1..120]]; // Marius A. Burtea, Feb 09 2020

Mathematica

Join[{0}, Table[Total[Transpose[FactorInteger[n^4 + 1]][[2]]], {n, 100}]] (* T. D. Noe, Aug 10 2011 *)
Join[{0},Table[PrimeOmega[n^4+1],{n,120}]] (* Harvey P. Dale, Sep 25 2012 *)

PARI

a(n) = bigomega(n^4+1); \\ Michel Marcus, Feb 09 2020

Formula

a(n) = A001222(A002523(n)) = bigomega(n^4+1) or Omega(n^4+1).